Hi, my 6-year-old daughter recently got a new betta, which she quickly named Rainbow Rock. After doing some research, it seemed like getting a small aquarium was the way to go, so we purchased a Marineland Eclipse 3 (we live in an apartment, so space is at a premium).

This is our first aquarium, and I am surprised at how noise the filter is. It's louder than I thought it would be -- sort of like the mechanical hum of a refrigerator. It can be heard from 20 feet away in a quiet room.

Like I said, we're brand new at this. Is this normal for an aquarium, or should it be quieter than this?

That tank has a Bio-Wheel filter, and in my experience, they tend to be noisier than other types. I've also had Whisper and AquaClear filters and they tend to be quieter unless something is wrong. I like the AquaClear the best, but I'm not familiar with the Eclipse 3 so I don't know how big the filter opening is.
You can measure the opening and see if anything else will fit.

Just want to add that a filter in a 3 gallon won't change the number of water changes you need to do (you still need to do 2 a week), just the amount of water (2x 50% changes instead of 1 50% and 1 100%).

I'm sorry I can't advise on what is normal for that brand. Some are dead quiet (like my Fluval Internals), some make bubble noises (sponge filters) and some make really annoying humming noises (like the one on my sister's AquaOne).

Do check the water level. Some filters get noisier the lower the water level is. As for quietness, aquariums do make noise. I have never had one be completely quiet. But give it a few weeks and you will get used to the white noise. In fact, whenever I shut off my filters in my fish room to do water changes I am amazed at how deathly quiet it is without the filters running.